Algebra 2 Semester 2 Final Review: Period 6 DHS

Exponential

100

A streaming platform promises to upgrade its video compression technology every year. Each new version reduces data usage by 12% compared to the previous version. If the current average data usage is 4.8 GB for a full movie stream, what will the average data usage be 7 years from now? (Round To 2 Digits!)

1.96 GB

200

Given these two points, (1, 0.75) and (0,3), find the exponential equation.

y = 3(0.25)^x

300

5x(-3x^2 * y^0 * z^-4)^2

45x^5 / z ^ 8

400

 Solve  27^(3x+5)=81^(4x+1)

x = 4/541

Logarithms

100

If  log b (25)=5.2 and log b(6)= 3.02    

Find:

a) log b (25/6)

b) log b (5)

a) 2.18

b) 2.6

200

2log 5 (p) +3log5 (r) -4log5 (s)

#5 is the base

log 5 ((p^2 * r^ 3) / s ^4)

#5 is the base

300

log5(3x+3)-log5(4)=log5(3x)

#5 is the base

x = 1/3

400

 2e^x - 17=42

x = ln(29.5), about 3.384

Trig Angles

100

Given that the angle  = 45 , find one positive and one negative coterminal angle.  

Positive Coterminal Angle: 405

Negative Coterminal Angle: -315

200

Sketch the angle, theta , and identify the reference angle and the quadrant where the terminal side is for: 

5pi/4

Quadrant |||:

300

 Given the right triangle, find the exact value of sec(theta)

         |

         | \

         |    \

 9      |       \        5 sqrt 3

         |          \

         |             \

         |                \
         |                  
         |_____theta _\

sec (theta) = 3 root 6 / 2

400

 Let  be the angle that corresponds to the point (-7,-24)  which is on a circle. Draw the diagram and find cot⁡(θ)  

cot⁡(θ) = -7/-24

Unit Circle Values

100

sin (5pi/6)

sin (5pi/6) = 1/2

200

tan(pi) = ?

0

300

tan (5pi/6)

1/-sqrt 3

400

cos (-2pi/3)

-1/2

T.A Transformations

100

Given parent function f(x) = 1/x and g(x) = 6f(x + 11) - 41, what is the domain and range?

Domain: all real numbers except x = -11

Range: all real numbers except y = -41

200

Given a parent function f(x), the transformed function g(x) can be found by applying the following transformations in the order listed 

reflect across the x axis, Translate 676767 units to the left, apply a horizontal stretch to the left by 6, translate 67 units down

-f (1/6 (x) + 676767) - 67

300

Given a parent function f(x) = x^3 and g(x) = 41f(x+ 34) - 6, Where are the domain and range of g(x)

Domain: All real numbers

Range: All real numbers

400

TA Special Problem:

Given the parent function of f(x) = csc(x) and g(x) = -365 tan (15x + 17) - 190, what are the domain, range, and amplitude.

YOU GUYS GOT THIS! LES GO!

• Reflection: The negative sign in front of 365 indicates a reflection over the x-axis.
• Vertical Stretch: The factor of 365 results in a vertical stretch by a factor of 365.
• Horizontal Compression: The factor of 15 inside the function results in a horizontal compression by a factor of 1/15 (the new period is 2pi/15)
• Phase Shift (Horizontal Shift): The  + 17/15 indicates a horizontal shift to the left by 17/15 units.
• Vertical Shift: The -190 at the end indicates a vertical shift downward by 190 units.